(a) Field of the Invention
The present invention relates to a method and an apparatus for cancellation of crosstalk signals using multi-dimensional coordination and vectored transmission. More particularly, the present invention relates to a method and an apparatus for cancellation of transmitted crosstalk signals by applying vectored transmission and multi-dimensional cable coordination to time and space through a sequential operation using a DFE (decision feedback equalizer) or preceding.
(b) Description of the Related Art
A digital subscriber line (DSL) technology provides transport of high-bit-rate digital information over public telephone lines. Recently, a new technique has been proposed to increase the overall data rate by coordinating all the lines in the same DSL cable.
Since crosstalk in DSL communication causes problems such as noise, the new technique causes many problems in a plurality of multi-user digital communication systems. For this reason, continuous and sub-optimal technologies are currently being used to cancel the crosstalk. The technologies for canceling the crosstalk affect transmission performance rather than bringing about operational improvement in the corresponding system.
The crosstalk problem has been researched in various contexts, such as in multi-channel signal processing and in using a corresponding minimum mean square error (MMSE) linear equalizer. In the absence of user coordination, transmitters of broader scope than Nyquist transmitters have been shown to provide a performance advantage over Nyquist-limited transmitters.
Recently, Cioffi proposed a modulation scheme that can cancel out FEXT (far-end crosstalk) by jointly processing the user signal at both the receiver and transmitter.
FIG. 1 is a diagram illustrating a data transmission structure between a DSL reception terminal and a DLS transmission terminal using a generalized decision feedback equalizer (G-DFE).
The data transmission structure using the G-DEF mainly includes a transmitting terminal 110 and a channel 120, and a receiving terminal 130.
The transmitting terminal 110 includes a transmission filter 112, and the transmission filter 112 includes a pre-distortion matrix A derived by a matched filter 132 of the receiving terminal 130. The u that is input to the transmission filter 112 is the pre-distorted data vector, and the signal that passes through the transmission filter 112 and is transmitted through the channel 120 is represented as x.
The channel 120 that transmits a signal between the transmitting terminal 110 and the receiving terminal 130 has an entire channel matrix H in a DSL cable. Further, an n value that is a noise vector is added to the signal transmitted through the channel 120. Therefore, the signal x transmitted from the transmitting terminal 110 is multiplied by a value of the entire channel matrix H, is added by the noise vector n, and is transmitted to the receiving terminal 130. That is, if the signal received by the receiving terminal 130 is assumed as y, the y is represented as Equation 1.y=Hx+n  (Equation 1)
The receiving terminal 130 includes the matched filter 132 and the G-DFE 134.
The matched filter 132 is a filter constructed using the entire channel matrix value H and the pre-distortion matrix value A of the transmission filter 112 in order to reliably receive the signal transmitted from the receiving terminal 130, and has an A*H* value. The signal that has passed through the matched filter 132 is represented as z, and the z is represented as Equation 2.z=Rfu+n′  (Equation 2)
In this case, Rf is A*H*HA and n′ is A*H*n. In addition, covariance of the noise n satisfies the condition Rnn=Rf. At this time, if Cholesky factorization is applied to Rf, it is represented as Equation 3.Rf=G**S0G  (Equation 3)
In this case, So is a diagonal matrix having a positive element, and G is a monic upper triangular matrix. At this time, when processing a z vector using So−1 G−* as an inverse matrix of G*So, it is represented as Equation 4.S0−1G−*z=Gu+S0−1G−*n′=Gu+e  (Equation 4)
In this case, G is an upper triangular matrix and an error e has uncorrelated components. In addition, the input signal u can be recovered by back-substitution combined with symbol-by-symbol detection. Accordingly, the G-DFE 134 having a decision feedback structure can be constructed to include a forward filter So−1G−* 142 and a feedback filter 1-G 148, as shown in FIG. 1. Further, the G-DFE 134 includes an adding unit 144 that adds a feedback signal transmitted from the feedback filter 148 and a signal transmitted from the decision forward filter 142 and a determining unit 146 that restores u∩ that is similar to the input signal u according to the signal transmitted from the adding unit 144.
In the structure of the G-DFE 134, the pre-distortion matrix A of the transmission filter 112 is represented as Equation 5.A=QmIDFTP  (Equation 5)
In this case, QmIDFT denotes an L-D expansion of a discrete Fourier transform (DFT) matrix QIDFT with N tones, and P denotes an L-D expansion of a permutation matrix. Therefore, Rf is factorized as Equation 6.Rf=P*QmDFTH*HQmIDFTP  (Equation 6)
At this time, when it is assumed that Hi,j is a circulant matrix of an entire channel matrix H, the condition Hi,j=QIDFTΛi,jQDFT is satisfied. In this case, since Λi,j is a diagonal matrix, Equation 6 can be represented as Equation 7.Rf=P*Λ*ΛP  (Equation 7)
In this case, Λi,j is the (i,j)-th element of Λ. The reordering Rf by P results in a block diagonal matrix as Equation 8.Rf=diag(Rf,1, Rf,2, . . . , and Rf,N)  (Equation 8)
In this case, Rf,i(i=1, 2, . . . , N) is an (L×L)-D matrix. At this time, the Cholesky factorization of Rf is represented as Equation 9.Rf=diag(G1*So,1G1, G2*So,2G2, . . . , and GN*So,NGN)  (Equation 9)
In addition, the decomposition as in Equation 10 is derived from Equation 9.P*ΛP=diag(Q1R1, Q2R2, . . . , and QNRN)  (Equation 10)
At this time, Qi (i=1, 2, . . . , N) is a unit matrix of (L×L)-D and Ri(i=1, 2, . . . , N) is an upper triangular matrix of (L (L)−D. Simple substitution proves the condition
      R    i    =            S              0        ,        1                    -                  1          2                      ⁢                  G        i            .      
Meanwhile, in the G-DFE 134, the feedback filter G=diag(G1, G2, . . . , GN) can be separated into N independent feedback filters, each of which operates at each tone. Here, the combination of the matched filter 132 and the decision forward filter is as Equation 11.S0−1G−*A*H=S0−1G−*P*Λ*QmDFT=S0−1G−1P*Λ*PP*QmDFT  (Equation 11)
Equation 12 is derived from Equation 11.
                                                                                          S                  0                                      -                    1                                                  ⁢                                  G                                      -                    *                                                  ⁢                                  A                  *                                ⁢                                  H                  *                                            =                            ⁢                                                S                  0                                      -                    1                                                  ⁢                                  G                                      -                    *                                                  ⁢                                  diag                  ⁡                                      (                                                                                            R                          1                          *                                                ⁢                                                  Q                          1                          *                                                                    ,                                                                        R                          2                          *                                                ⁢                                                  Q                          2                          *                                                                    ,                      ⋯                      ⁢                                                                                          ,                                                                        R                          N                          *                                                ⁢                                                  Q                          N                          *                                                                                      )                                                                                                                                        ⁢                                                P                  *                                ⁢                                  Q                  mDFT                                                                                                        =                            ⁢                                                S                  0                                      -                    1                                                  ⁢                                  G                                      -                    *                                                  ⁢                                                      diag                    ⁡                                          (                                                                                                    G                            1                            *                                                    ⁢                                                      S                                                          o                              ,                              1                                                                                      1                              2                                                                                                      ,                                                                              G                            2                            *                                                    ⁢                                                      S                                                          o                              ,                              2                                                                                      1                              2                                                                                                      ,                        ⋯                        ⁢                                                                                                  ,                                                                              G                            N                            *                                                    ⁢                                                      S                                                          o                              ,                              N                                                                                      1                              2                                                                                                                          )                                                        ·                                                                                                                      ⁢                                                diag                  ⁡                                      (                                                                  Q                        1                        *                                            ,                                              Q                        2                        *                                            ,                      ⋯                      ⁢                                                                                          ,                                              Q                        N                        *                                                              )                                                  ⁢                                  P                  *                                ⁢                                  Q                  mDFT                                                                                                        =                            ⁢                                                diag                  ⁡                                      (                                                                  S                                                  o                          ,                          1                                                                          1                          2                                                                    ,                                              S                                                  o                          ,                          2                                                                          1                          2                                                                    ,                      ⋯                      ⁢                                                                                          ,                                              S                                                  o                          ,                          N                                                                          1                          2                                                                                      )                                                  ·                                                                                                      ⁢                              diag                ⁢                                  (                                                            Q                      1                      *                                        ,                                          Q                      2                      *                                        ,                    ⋯                    ⁢                                                                                  ,                                          Q                      N                      *                                                        )                                ⁢                                  PQ                  mDFT                                                                                        (                  Equation          ⁢                                          ⁢          12                )            
However, as described above, there is a problem in the data transmission structure between the DSL reception terminal and the xDSL service in which a type of a cable line is different. Further, there is a problem in that near-end cross-talk (NEXT) occurs.